title: Reduced-order models for closed-loop wake control.
abstract: We review a strategy for low- and least-order Galerkin models suitable for the design of closed-loop stabilization of wakes. These low-order models are based on a fixed set of dominant coherent structures and tend to be incurably fragile owing to two challenges. Firstly, they miss the important stabilizing effects of interactions with the base flow and stochastic fluctuations. Secondly, their range of validity is restricted by ignoring mode deformations during natural and actuated transients. We address the first challenge by including shift mode(s) and nonlinear turbulence models. The resulting robust least-order model lives on an inertial manifold, which links slow variations in the base flow and coherent and stochastic fluctuation amplitudes. The second challenge, the deformation of coherent structures, is addressed by parameter-dependent modes, allowing smooth transitions between operating conditions. Now, the Galerkin model lives on a refined manifold incorporating mode deformations. Control design is a simple corollary of the distilled model structure. We illustrate the modelling path for actuated wake flows.
authors.affiliation: Northeastern University, 440 Dana Building, 360 Huntington Avenue, Boston, MA 02115-5000, USA. tadmor@ece.neu.edu
authors.forename: Gilead
authors.initials: G
authors.lastname: Tadmor
authors.forename: Oliver
authors.initials: O
authors.lastname: Lehmann
authors.forename: Bernd R
authors.initials: BR
authors.lastname: Noack
authors.forename: Laurent
authors.initials: L
authors.lastname: Cordier
authors.forename: Joël
authors.initials: J
authors.lastname: Delville
authors.forename: Jean-Paul
authors.initials: JP
authors.lastname: Bonnet
authors.forename: Marek
authors.initials: M
authors.lastname: Morzyński